Double helical waveguide feed with linear slot array for frequency scanning



Oct. 1, 1963 M. H. BODMER 3,105,968 DOUBLE HELICAL WAVEGUIDE FEED WITH LINEAR SLOT ARRAY FOR FREQUENCY SCANNING Filed March 24, 1960 3 Sheets-Sheet 1 Fig.2

PH Av; I Prior Art Fig.4-

INVENTOR. MAXIMILIAAN H. BODMER 2M m AGENT Oct. 1, 1963 M. H. BODMER DOUBLE HELICAL WAVEGUIDE FEED WITH LINEAR SLOT ARRAY FOR FREQUENCY SCANNING asheets-sheet 2 Filed March 24, 1960 Prior fil-t INVENTOR. MAXIMILIAAN H. BODMER AGENT Oct. 1, 1963 M. H. BODMER 3, 8

DOUBLE HELICAL WAVEGUIDE FEED WITH LINEAR SLOT ARRAY FOR FREQUENCY SCANNING Filed March 24, 1960 3 Sheets-Sheet 5 INVENTOR.

MAXIMILIAAN H. BODME R M AGENT United States Patent 3,165,968 DOUBLE HELICAL WAVEGUIDE FEED WITH LINEAR SLGT SCANNING Maximiliaan H. Bodmer, Hengelo, Netherlands, assignor to North American Philips Company, Inc, New York, N.Y., a corporation of Delaware Filed Mar. 24, 1960, Ser. No. 17,294 Claims priority, application Netherlands Mar. 25, 1959 8 Claims. (Cl. 343-771) The invention relates to an aerial system for radiating concentrated high frequency field energy of the type having a number of radiating slots, situated in a single row and fed by the same wave guide. Each part of the wave guide situated between two successive slots fed by the said wave guide is carried in such a way around an axis parallel to the row of slots that the length of each part of the wave guide between two successive slots fed by this wave guide is substantially larger than the direct distance between these slots, and a travel ling wave propagated through the wave guide passes all radiating slots in the wave guide in the same sense.

Aerial systems of the type in which the wave guide is helically arranged between two successive slots are well known. The beam generated by such an aerial system swings around an axis perpendicular to the row of slots when the feed frequency changes. Such aerials are employed for generating a scanning beam, which is narrow in the scanning direction. Their special construction, whereby the wave guide length between two successive slots is substantially larger than the direct distance between the slots, permits a reduction in the direct distance to such an extent that the radiation pattern exhibits only a single beam, while the wave guide length present between two successive slots in the wave guide is still fairly large, so that a scanning motion of the beam through a substantial and sufficient angle can be caused by a permissible frequency swing.

It is the object of the invention to build an aerial system operating according to the above principles and by means of which two similar and partially overlapping beams can be generated, which beams both perform a substantially corresponding scanning motion as a result of changes in the feed frequency, and wherein the angle between these beams in the scanning direction is small and shows no more than a slight change as a function of the feed frequency. Such double scanning beams are used in mono-pulse radar systems. For an axis around which the direction of a target must be established, such a radar system generates two overlapping beams, which are mutually displaced around said axis. The situation of a target hit by the :two beams with respect to the direction of these beams is established by comparing the strengths of the echoes simultaneously received from the target by way of these two beams.

According to the invention the aerial system is built so as to possess a second set of slot radiators substantially situated in the same row as the slots already mentioned, and fed by a second wave guide. The second wave guide is carried around the aerial axis between each pair of successive slots fed by the second wave guide. In a cross section of the system near the row of slot radiators, a cross section of the one and a cross section of the other wave guide alternately occur, and the difference between the phase of thehigh frequency energy at the beginning and the phase at the end of a part of the one wave guide between two successive slot radiators fed by this wave guide differs from the corresponding difference occurring in the corresponding part of the other wave guide.

In the simplest form of an aerial system according to 3,105,968 Patented Oct. 1, 1963 the invention the difference between the phase shift (p in a part of the one wave guide situated between two successive slots fed by this guide and the phase shift o occurring in the corresponding part of the other wave guide, results from a difference in length of the parts of these wave guides situated between corresponding successive slot radiators. This form will give fairly satisfactory results, but has the disadvantage that the difference in phase shift, and consequently the angle between the two beams, changes perceptibly as a funtcion of frequency.

The difference in phase shift can also be obtained by mounting one or more diaphragms in each part of one of the wave guides situated between two successive slots in this wave guide, each of which diaphragms reduces the same dimension of the wave guide so that all diaphragms, either reduce the largest dimension, or the smallest dimension, of the wave guide and consequently operate as an inductive shunt or a capacitive shunt, thereby causing an extra phase shift. The two wave guides can in this case have the same shape, which simplifies the manufacture of the aerial. The difference in phase shift is caused by the diaphragms in the one wave guide. Also in this case, however, the angle between the two beams perceptibly changes as a function of frequency, so that this angle varies when the beam scans. A substantially constant angle between the beams can be obtained by means of the aerial construction described below. In each part situated between two successive slots in one of the wave guides one or more diaphragms are mounted which reduce the largest dimension of this guide and consequently operate as a shunt inductance. In each part of the other wave guide situated between two successive slots in this guide, one or more diaphragms are mounted which reduce the smallest dimensions of the wave guide and consequently operate as a shunt capacity. The first type of diaphragm causes a phase lag, the second type a phase advance, so that even in the case of the parts between two successive slots in the two guides having the same length there will be a difference between the phase shift occurring between two successive slots in the one wave guide and the phase shift occurring between the corresponding slots in the other wave guide. Consequently the direction of the beam radiated by the slots fed by the one wave guide will differ from the direction of the beam radiated by the slots fed by the other wave guide. The phase lag as well as the phase advance caused by the diaphragms change as a function of frequency. When the frequency increases the phase lag decreases and the phase advance increases and the reverse, so that the said changes in the phase shift occur in the same sense. Preferably the dimensions of the diaphragms are such that, if the system is fed by one certain frequency situated within the frequency range covered by the frequency swing, the phase lag caused between two successive slots by the diaphragms of the one type is equal to the phase advance Y caused by the diaphragms of the other type between two successive slots. It appears then, that the changes caused by afrequency variation in the phase shifts caused by the two types of diaphragms are also practically equal within a fairly large frequency range. Preferably the aerial system is built in such a way that the lengths of the part of the wave guides situated between corresponding slots in the two guides are equal. The changes in the phase shifts occurring in the parts of the two wave guides situated between corresponding slots caused by a frequency variation, will then also be equal. Consequently the phase shift between the energy radiated by two successive slots of one wave guide and the direction of the beam radiated by the slots in this guide will change as a function of frequency; but the difference between the phase shift in a part between two slots of the one wave guide and the phase shift in the part of the other wave guide between the corresponding slots remains practically unchanged when the frequency changes, so that the angle between the two scanning beams radiated by the aerial system will be practically independent of the frequency and of the direction of the beams while scanning. This has the advantage that the sensitivity of a radar apparatus operating with the aerial system to a deviation of a target will remain practically constant throughout the scanned area.

The invention will now be explained by describing examples of the aerial according to the invention with reference to the drawings.

FIGURES l, 2 and 3 show a part of a known aerial system having slot radiators fed by a helically wound wave guide for radiating a single scanning beam.

FIGURES 4, 5 and 6 show a part of an aerial system according to the invention for radiating two overlapping scanning beams.

FIGURE 7 shows the cross section of an aerial system according to the invention, the cross section traverse to the beam direction of which is reduced.

FIGURE 8 shows an arrangement for feeding the two wave guides of an aerial system according to the FIG- URES 4, 5 and 6. 7

FIG. 9 is a cross-sectional view of an aerial according to another embodiment of the invention.

In order to facilitate the comprehension of the operation of the aerial according to the invention an aerial system of the same kind, which, however, is only able to generate one single beam, will first be described with reference to the FIGURES 1, 2 and 3.

FIGURE 1 shows this aerial system partly in front elevation, partly in cross section, FIGURE 2 shows a cross section passing through the slot radiators of the same system and FIGURE 3 a perspective view of the aerial system. The system comprises one single feeding wave guide, which is helically Wound around !an axis 16, with its smallest dimension situated radially. The cross section is indicated by the indices 8, 9, 1d and 11 in FIG. 1 and by the indices 12, 13, 14 and 15 in FIG. 2. In FIG. 2 the wave guide is shown by dotted lines, while in FIG. 1 the centredine of its outer wall is shown by a dotted line. A number of slot radiators (1, 3, 5, 7), onein each winding of the wave guide, are situated on the same :generatrix of the cylindrical outer surface of the system. The centre of each slot radiator is situated on the centre-line of the wall of the wave :guide; but its direction does not coincide with the said centre-line. The part of the energy flowing through the wave guide radiated by such a slot radiator increases as the angle be tween the slot radiator and the said centre-line is increased. It is desirable for 'all slot radiators to radiate equal quantities of energy. The energy quantity flowing through the wave guide is, however, reduced by each radiator receiving energy from the wave guide. Consequently the slot situated nearest to the end of the wave guide fed by the transmitter must receive only a small part of the energy flowing past it through the wave guide, and the angle between this slot and the centre-line should be small; this angle should be increased as the slot is situated farther from the fed end of the wave guide. The last slot encloses a large angle with the centre-line. Only a very small residual energy passes this last slot, i.e. only a few percent of the energy supplied to the system, and this residual energy is dissipated in a load of some well known construction, the impedance of which substan tially equals the characteristic impedance of the wave guide system, so that reflections are avoided.

The electrical vector of the radiation possesses a substantial component in the direction of the line connectlog the slots, but undesirable coupling between successive slots isprevented by grooves (2, 4, 6) in the aerial surface between two successive slot radiators. The depth '4 of these grooves corresponds to about a quarter wave length in the frequency range of the radiated energy.

If the radiation is to be concentrated in a second direction the radiator system shown in FIGS. 1, 2 and 3 is mounted in such a way in front of a parabolic cylindrical reflector, that the line through the centres of the radiators coincides with the focal line of the reflector.

It need not be explained that the angle between the beam and the axis of the system changes when the frequency of the energy supplied to the system changes. In order to give an idea of the performance of such an aerial system it may be stated here that the beam of an aerial with a cross section of 7 or 8 inches, fed by a frequency of 3000 megacycles showing a swing of 200 megacycles, will swing through an angle of approximately 30.

FIGS. 4, 5 and 6 show an aerial system according to theinvention. This system is able to radiate two scanning beams diflering slightly in direction. FIG. 4 shows the system partly in front elevation and partly in cross section, FIG. 5 shows the system in a cross section passing through the nadiator slots, and FIG. 6 shows a perspective view of the system. The aerial system comprises two wave guides, the wave guide A and the wave guide B, wound like a screw with double thread. In the cross section of the system, therefore, cross sections of the wave guide A and the wave guide B alternate. In the same way in the row of slot radiators slots a in the wave guide A alternate with slots b in the wave guide B. Because it is necessary for the distance between two successive slots in the same wave guide to be smaller than the wavelen the wave guides must be wound in such a way that their largest cross section dimensions are situated radially with respect to the axis of the aerial, the slot radiators-being-situated in the narrow walls of the Wave guides, as may be seen in the figures. A slot only radiates part of the energy flowing in a cross section :of a wave guide near this slot, this part is determined by the angle between the slot and the axis of the wave guide. Near the end of the wave guide fed by the transmitter only a small part of this energy is radiated, while near the other end a large part of it is radiated. The free ends of the wave guides are terminated by a load, which dissipates the residualenergy, and the impedance of which substantially equals the characteristic impedance of the wave guide, so that reflections are avoided. In each winding turn of the wave guide A, in the part situated between two successive slots of this guide, one

or more diaphragms 501 are mounted, which reduce the smallest cross section dimension of the wave guide and, therefore, openate as a shunt capacitance thus causing a phase advance of the energy. In each winding turn of the wave guide B in the part situated between two successive slots of this wave guide, one or more diaphr agms 502 are mounted, which reduce the largest cross section dimension of the wave guide and, therefore, operate as a shunt inductance, and cause a phase lag of the energy.

The electrical vector of the radiation shows only a relatively small component in the direction of the row of radiator slots, so that special means, such as damping grooves for reducing \the coupling between successive slots, are less important. In the example shown in the figures no such grooves are present.

When the two wave guides are fed by the same varying frequency, the .two beams. radiated by the slots present in the two wave guides swing around an axis perpendicular to the row of slots. During this swinging motion the angle between the two beams remains practically constant.

Aerials able to produce two beams which scan by swinging around the same axis While having a slightly difierent direction around the said axis are generally used in the following way. The two radiator systems are fed by one and the same transmitter in such a way that beams with the same amplitude and phase are radiated. Two receivers cooperate with the aerial. To one a shunt capacitance and cause a phase advance.

of these receivers a quantity of energy is supplied which is proportional to the sum of the quantities of energy received simultaneously by the two radiator systems and supplied by way of their input wave guides. To the other receiver, the diiferential receiver, a quantity of energy is supplied which is proportional to the diiier- 'ence in the said energy quantities received by the radiator systems. The presence of a target in the beam is shown by the first mentioned sum receiver, the moment at which the beam occupies a well defined position with respect to the target is indicated by the difierential receiver, for as long as echo energy is received (which is shown 'by the sum receiver) in only one position of the :beam with respect to the target, no energy is supplied to the differential receiver. For this purpose the aerial system must be fed by an arrangement which, on the one hand divides the energy received from the transmitter equally and With the same phase between the two wave guides of the aerial system, while on the other hand one output element of this arrangement supplies an energy quantity which cor-responds to the sum mentioned above, and another output element supplies an energy quantity which corresponds to the difference mentioned. Various arrangements can be applied for this purpose, one of which will be described with reference to FIG. 8. The arrangement shown in FIG. 8 comprises a short slot hybrid consisting of two waveguides, the largest cross sectional dimensions of which are parallel to the plane of the drawing and which possess a part with a common narrow wall. An opening 801 is present in this wall. The transmitter energy is supplied to the arrangement with an amplitude E by way of the wave guide stub Z. The slot 801 divides this energy equally between the two wave guides connected by it. The amplitude in the two wave guides is consequently direction of the wave guide B remains unchanged, the

energy passing through the slot shows a phase advance through 90 and flows in the direction of the wave guide A. In the wave guide B, which is connected to the wave guide B of the aerial system, a number of diaphragms 802 are mounted, which reduce the smallest dimension of the wave guide and therefore operate as The dimensions of these diaphragms are such that a phase advance of 45 occurs. In the other wave guide A, in which the energy was already subjected to a phase advance of 90, a number of diaphragnis 306 are present, which reduce the largest dimension of the wave guide, thus acting as a shunt inductance and causing a. phase lag. The dimensions of the diaphragms are such that the said phase lag is equal to 45. Consequently energy quantities with an amplitude of both showing a phase advance of 45 with respect to the energy furnished by the transmitter, are supplied "by way of the wave guides A and B' to the wave guides A and B of the aerial system. The two wave guides of the aerial system are in this way fed by wave energy with the same phase and amplitude. Assume that echo energy received by the aerial system is returned by way of the two wave guides, the amplitude in wave guide A being E and that in wave guide B being E Both wave energies have the same phase because they result from echoes caused by the transmitting pulse hitting one single target and having covered the same distance. After having passed the diaphragms, the energy E shows a phase lag of 45 and the energy E a phase advance of 45. Both energy quantities are divided by the slot parts between the curved parts.

801 between the wave guides Z and V. A passage through the slot always causes a phase advance iOf The wave guide Z receives an energy with an amplitude with a phase advance of 45 as well as an energy with an amplitude with the same phase advance. The energy supplied by way of wave guide Z is consequently proportional to the sum of the energies received by the two radiator systems with the wave guides A, and B. A TR switch of well known construction may be inserted between the Wave guide Z and the transmitter, and directs this sum energy to the sum receiver. The wave guide V receives, from the wave guide A, an energy with an amplitude and a phase lag of 45 while it receives energy with an amplitude with a phase advance of from the wave guide B. These energy quantities are, therefore, in opposition and the wave gulide V supplies an energy which is proportional to the difference in the energies received by the two parts of the aerial system. The wave guide V is connected to the differential receiver.

In some cases a larger stroke of the beam, for instance a stroke through 60, may be required. Because of the restriction to which the frequency swing is subjected, this larger stroke should be obtained with the same frequency swing. This requires a greater length of the wave guide between successive slots.

Without special measures the diameter of the aerial system must then be increased which will be undesirable if the aerial cooperates with a parabolic cylindrical reflector for concentration of the beam in a second direction. FIG. 7 shows the cross section of an aerial system in which the dimensions perpendicular to the beam are reduced. The lengthening of the wave guides between successive slots is obtained by inserting straight In this case it is not necessary for the slots to be situated inthe plane through "the two axes 701'and 702 of the curved parts.

In the examples described above the wave guides are helically'shaped. This is, however, by no means necessary. It would, for instance, be possible for the wave guides to remain perpendicular to the axis of the system in the vicinity of the slots, the shifting to the height of the next slot being eifected in the remaining part of a winding of the guide. Apart from being used in order to reduce the dimensions of the system traverse to the beam, straight parts in the wave guides can-also (be applied in order to simplify the construction, especially if the system is manufactured by casting. The system shown in FIG. 7, for instance, may consist of circular wave guide parts connected by straight parts in which the shifting to the height of the next slot occurs. The cores used in casting the system may then consist of simple straight and circular parts. 7

Preferably the wave guide system is cast in two or three longitudinal parts limited by flat surfaces. These parts are connected by soldering or welding. The strength and rigidity are preferably increased by supporting the system on a bar situated in the inner space of the system. I

FIG. 9 illustrates another embodiment of the aerial system of the invention in which the difierence between the phase shift in a part of one waveguide A between successive slots a in the waveguide A, and the phase shift in the other waveguide B between successive slots b, results from a difference between the physical lengths of the waveguides A and B "between their respective slots a and b. Thus, in the arrangement of FIG. 9, the turns of the waveguide B are shorter, for example, by having a smaller radius, than the turns of the waveguide A.

In the examples shown in the figures, the coupling of the slots with the inner space of the wave guides is in phase. It would also be possible to couple the said slots in opposition, for which purpose the slots fed by the same wave guide must alternately deviate in opposite sense from the position in which no energy passes the slot. It must be observed that, in order to avoid strong reflections and standing waves, the distance between two successive slots in the same wave guide which are coupled in phase should at no frequency pertaining to the range covered by the frequency swing be equal to a whole number of wave lengths, and that the distance between successive slots coupled in opposition should never be equal to an uneven number of half wave length.

I claim:

1. An aerial for radiating a pair of similar and partially overlapping scanning beams of concentrated high frequency field energy comprising a longitudinally extending system of alternate turns of a first and second Waveguide means about a common line, each turn of said first and second waveguide means having an external radiating" slot, said slots forming a single row of slots, the turns of said first and second waveguide means being longer than the direct distance between adjacent slots of the same waveguide means, said aerial having means providing a different phase relationship between adjacent slots of said first waveguide means and corresponding adjacent slots of said second waveguide means.

2. An aerial for radiating a pair of similar and partially overlapping scanning beams of concentrated high frequency field energy comprising a longitudinally extending system of alternate turns of a first and second waveguide means about a common line, each turn of said first and second waveguide means having an external radiating slot, said slots forming a single row of slots, the turns of said first and second waveguide means being longer than the direct distance between adjacent slots of the same waveguide means, the length of the turns of said first waveguide means between slots differing from the length of turns of adjacent second waveguide turns between slots.

3. An aerial for radiating a pair of similar and partially overlapping scanning beams of concentrated high frequency field energy comprising a longitudinally extending system of alternate turns of a first and second waveguide means about a common line, each turn of said first and second waveguide means having an external radiating slot, said slots forming a single row of slots, the turns of said first and second waveguide means being longer than the direct distance between adjacent slots of the same waveguide means, and diaphragm means in each turn of said first waveguide means, said diaphragm means reducing the same dimension of the first waveguide means in each turn of said first waveguide means.

4 An aerial for radiating a pair of similar and partially overlapping scanning beams of concentrated high frequency field energy comprising a longitudinally extending system of alternate turns of a first and second waveguide means about a common line, each turn of said first and second waveguide means having an external radiating slot, said slots forming a single row of slots, the turns of said first and second waveguide means being longer than the direct distance between adjacent slots of the same waveguide means, and diaphragm means in each turn of said first and second waveguide means, said diaphragm means reducing the same dimension of said tially overlapping scanning beams of concentrated high frequency field energy comprising a longitudinally extending system of alternate turns of .a first and second waveguide means about a common line, each turn of said first and second waveguide means having an external radiating slot, said slots forming a single row of slots, the turns of said first and second waveguide means being longer than the direct distance between adjacent slots of the same Waveguide means, each turn of' said first waveguide means'b-etween slots having a length substantially equal to the length of each adjacent turn of said second waveguide means between slots, and means providing a diiferent phase relationship between adjacent slots of said first waveguide means and corresponding adjacent slots of said second waveguide means.

7. An aerial system for radiating a pair of similar and partially overlapping beams of concentrated high frequency field energy, said aerial system comprising a first group of longitudinally spaced apart turns of first .wavegu-ide means about a line, a second group of longitudinally spaced apart turns of second waveguide means about said line, the turns of said second group being positioned between adjacent turns of said first group,

whereby the turns of said, first and second waveguide means alternate longitudinally of said aerial system, a slot in the surface of each turn of said waveguide means away from said line, said slots being aligned to form a single row of slots, the length of each turn of said waveguide means being greater than the direct distance between adjacent slots of the respective waveguide means, and means providing a difference between the phase relationship of high frequency energy between adjacent slots of said first waveguide means and the phase relationship of high frequency energy between adjacent slots of said second waveguide means.

8. An aerial system for radiating a pair of similar and partially overlapping beams of concentrated high frequency field energy of a given frequency range, said aerial system comprising a first group of longitudinally spaced apart turns of a first waveguide about a line, a second group of longitudinally spaced apart turns of a second waveguide turns about said line, the turns of said second group being positioned between adjacent turns of said first group, whereby the turns of said first and second waveguide :means alternate longitudinally of said aerial systent, said first and second waveguide means having crosssectional dimensions whereby they are capable of transmitting energy in said given frequency range, the lengths of the turns of said first and second waveguide means being equal, a slot in the surface of each turn of said waveguide means away from said line, said slots being aligned to form a single row of slots, the length of each turn of said waveguide means being greater than the direct distance between adjacent slots of the respective waveguide means, and diaphragm means in each turn of said first and second waveguide means, said diaphragm means reducing the same dimension of said first waveguide means in each turn thereof and reducing the other dimension of said second waveguide means in each'turn thereof, said diaphrams being proportional to provide a phase advance in each turn of said first waveguide means equal to the phase lag in each turn of said second waveguide 9 means for a given frequency within said given frequency 2,623,121 range. 2,676,257 2,743,440 References Ciied 1n the file of thls patent 2 1 90 UNITED STATES PATENTS 5 2,607,031 Denis et a1. Aug. 12, 1952 2,616,046 Marston et a1 Oct. 28, 1952 3,033

10 Loveridge Dec. 23, 1952 Hebens-treit Apr. 20, 1954 Riblet Apr. 24, 1956 (Draw-ford et a1 Oct. 22, 1957 FOREIGN PATENTS France June 18, 1951 

7. AN AERIAL SYSTEM FOR RADIATING A PAIR OF SIMILAR AND PARITALLY OVERLAPPING BEAMS OF CONCENTRATED HIGH FREQUENCY FIELD ENERGY, SAID AERIAL SYSTEM COMPRISING A FIRST GROUP OF LONGITUDINALLY SPACED APART TURNS OF FIRST WAVEGUIDE MEANS ABOUT A LINE, A SECOND GROUP OF LONGITUDINALLY SPACED APART TURNS OF SECOND WAVEGUIDE MEANS ABOUT SAID LINE, THE TURNS OF SAID SECOND GROUP BEING POSITIONED BETWEEN ADJACENT TURNS OF SAID FIRST GROUP, WHEREBY THE TURNS OF SAID FIRST AND SECOND WAVEGUIDE MEANS ALTERNATE LONGITUDINALLY OF SAID AERIAL SYSTEM, A SLOT IN THE SURFACE OF EACH TURN OF SAID WAVEGUIDE MEANS AWAY FROM SAID LINE, SAID SLOTS BEING ALIGNED TO FORM A SINGLE ROW OF SLOTS, THE LENGTH OF EACH TURN OF SAID WAVEGUIDE MEANS BEING GREATER THAN THE DIRECT DISTANCE BETWEEN ADJACENT SLOTS OF THE RESPECTIVE WAVEGUIDE MEANS, AND MEANS PROVIDING A DIFFERENCE BETWEEN THE PHASE RELATIONSHIP OF HIGH FREQUENCY ENERGY BETWEEN ADJACENT SLOTS OF SAID FIRST WAVEGUIDE MEANS AND THE PHASE RELATIONSHIP OF HIGH FREQUENCY ENERGY BETWEEN ADJACENT SLOTS OF SAID SECOND WAVEGUIDE MEANS. 